Given the function:
[tex]f(x)=\sqrt[]{3x+6}[/tex]to find the inverse function, first we have to set f(x) = y, and the solve for y. In this case, we have the following:
[tex]\begin{gathered} y=f(x) \\ \Rightarrow y=\sqrt[]{3x+6} \\ \Rightarrow y^2=3x+6 \\ \Rightarrow y^2-6=3x_{} \\ \Rightarrow\frac{y^2-6}{3}=x \end{gathered}[/tex]therefore, the inverse function is:
[tex]f^{-1}(x)=\frac{x^2-6}{3}[/tex]